Hom $ω$-categories of a computad are free
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913576940208128 |
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| author | Benjamin, Thibaut Markakis, Ioannis |
| author_facet | Benjamin, Thibaut Markakis, Ioannis |
| contents | We provide a new description of the hom functor on weak $ω$-categories, and we show that it admits a left adjoint that we call the suspension functor. We then show that the hom functor preserves the property of being free on a computad, in contrast to the hom functor for strict $ω$-categories. Using the same technique, we define the opposite of an $ω$-category with respect to a set of dimensions, and we show that this construction also preserves the property of being free on a computad. Finally, we show that the constructions of opposites and homs commute. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_01611 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hom $ω$-categories of a computad are free Benjamin, Thibaut Markakis, Ioannis Category Theory Logic in Computer Science 18N65, 18M90, 18N30 We provide a new description of the hom functor on weak $ω$-categories, and we show that it admits a left adjoint that we call the suspension functor. We then show that the hom functor preserves the property of being free on a computad, in contrast to the hom functor for strict $ω$-categories. Using the same technique, we define the opposite of an $ω$-category with respect to a set of dimensions, and we show that this construction also preserves the property of being free on a computad. Finally, we show that the constructions of opposites and homs commute. |
| title | Hom $ω$-categories of a computad are free |
| topic | Category Theory Logic in Computer Science 18N65, 18M90, 18N30 |
| url | https://arxiv.org/abs/2402.01611 |